L is the natural length of the spring AD. AC is length 4.

Set L to be 3. How many stable positions are there? (You can drag D to different start points on the line and see where it goes.)

Try dragging B to rotate the line. How does it affect the stable positions?

Now change L to 6, but move B so the line is horizontal. How many stable positions are there?

Now move B so that the line slopes down from D to C. Observe that D moves slowly towards C until the stable point disappears and it moves "catastrophically" to the other stable point.

This example is from Steven H Strogatz Nonlinear Dynamics and Chaos